EJP Reading Tools

Subcritical contact processes seen from a typical infected site

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Subcritical contact processes seen from a typical infected site
2.	Creator	Author's name, affiliation, country	Anja Sturm; University of Göttingen; Germany
2.	Creator	Author's name, affiliation, country	Jan M. Swart; Institute of Information Theory and Automation of the ASCR; Czech Republic
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Contact process, exponential growth rate, eigenmeasure, Campbell law, Palm law, quasi-invariant law.
3.	Subject	Subject classification	Primary: 82C22 Secondary: 60K35, 82B43.
4.	Description	Abstract	What is the long-time behavior of the law of a contact process started with a single infected site, distributed according to counting measure on the lattice? This question is related to the configuration as seen from a typical infected site and gives rise to the definition of so-called eigenmeasures, which are possibly infinite measures on the set of nonempty configurations that are preserved under the dynamics up to a time-dependent exponential factor. In this paper, we study eigenmeasures of contact processes on general countable groups in the subcritical regime. We prove that in this regime, the process has a unique spatially homogeneous eigenmeasure. As an application, we show that the law of the process as seen from a typical infected site, chosen according to a Campbell law, converges to a long-time limit. We also show that the exponential decay rate of the expected number of infected sites is continuously differentiable and strictly increasing as a function of the recovery rate, and we give a formula for the derivative in terms of the long time limit law of the process as seen from a typical infected site.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Work sponsored by GAČR grants 201/09/1931 and P201/12/2613.
7.	Date	(YYYY-MM-DD)	2014-06-23
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/2904
10.	Identifier	Digital Object Identifier	10.1214/EJP.v19-2904
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
15.	Rights	Copyright and permissions	The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available. Summary of the Creative Commons Attribution License You are free to copy, distribute, display, and perform the work to make derivative works to make commercial use of the work under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.